How to copy a Cutout from one Object to another
Based on the instructions provided by Leander, this is how a copied a hole from one object and added to another similar object.  Note - there are other easier ways to do this like Knife Project or simply making one object and duplicating it. But I wanted to learn.


Select object to copy from and tab into edit mode

Select vertices outlining the feature (hole) to copy.  In this case also selecting the faces which will replace the faces on the object to be modified.
Shft-D to duplicate the vertices and move them to the side

Separate the duplicate vertices from the original object by clicking P and selecting by loose parts

I should have done this next. Select other object and tab into edit mode. Select faces to be replaced and delete them. Exit edit mode.

Select duplicate vertices and Set Origin to Geometry

Select object to be modified and center cursor on object Shft-S cursor to selection
Select duplicate vertices and Shft-S selection to cursor
Add new object to duplicate vertices Shft-LMB
Join vertices and new object Ctrl-J join